According to the conventional process for producing polymers of polycondensation series of polyethylene terephthalate, etc., raw materials terephthalic acid and ethylene glycol are fed to a mixing tank in an appropriate proportion for esterification and the mixture is then fed to esterification reactor tanks through a pump. In the esterification step, 2 or 3 stirring tanks each provided with stirring vanes are provided in series and a water effluent as a by-product is separated in a distillation column. A prepolymerization step follows, where a plurality of vertical stirring tanks or horizontal stirring tanks are provided, and a final polymerization step follows, where a horizontal stirring tank is provided. The tanks of these polymerization steps are each provided with a condeser for removing an effinent ethylene glycol as a by-product, and are operated in a reduced pressure atmosphere. In the conventional process for producing polyester there are 4 to 6 reactor tanks, each of which is provided with strring vanes and its power source and further provided with a distillation column or a condenser for separating and removing the by-product. Furthermore, the polymerization steps are operated in a reduced pressure atmosphere, and thus the necessary additional vacuum means for generation of a reduced pressure is required. That is, the operation of the apparatus requires a higher maintenance cost and a higher apparatus cost. One example of the related art is disclosed in JP-A 7-207009, where each tank is provided with stirring vanes and is vacuum-controlled, and thus its running or operation is complicated. That is, improved apparatus and process with a higher efficiency throughout the apparatus and economical operation based on energy saving throughout the apparatus have been so far desired for the production of high molecular weight polyester.